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We study the algorithmic complexity of computing persistent homology of a randomly generated filtration. Specifically, we prove upper bounds for the average fill-in (number of non-zero entries) of the boundary matrix on \v{C}ech, Vietoris--Rips and Erd\H{o}s--R\'enyi filtrations after matrix reduction. Our bounds show that the reduced matrix is expected to be significantly sparser than what the general worst-case predicts. Our method is based on previous results on the expected Betti numbers of the corresponding complexes. We establish a link between these results and the fill-in of the boundary matrix. In the $1$-dimensional case, our bound for \v{C}ech and Vietoris--Rips complexes is asymptotically tight up to a logarithmic factor. We also provide an Erd\H{o}s--R\'enyi filtration realising the worst-case.

Building upon the exact methods presented in our earlier work [J. Complexity, 2022], we introduce a heuristic approach for the star discrepancy subset selection problem. The heuristic gradually improves the current-best subset by replacing one of its elements at a time. While we prove that the heuristic does not necessarily return an optimal solution, we obtain very promising results for all tested dimensions. For example, for moderate point set sizes $30 \leq n \leq 240$ in dimension 6, we obtain point sets with $L_{\infty}$ star discrepancy up to 35% better than that of the first $n$ points of the Sobol' sequence. Our heuristic works in all dimensions, the main limitation being the precision of the discrepancy calculation algorithms. We also provide a comparison with a recent energy functional introduced by Steinerberger [J. Complexity, 2019], showing that our heuristic performs better on all tested instances.

In this work, we introduce DeepIPC, a novel end-to-end model tailored for autonomous driving, which seamlessly integrates perception and control tasks. Unlike traditional models that handle these tasks separately, DeepIPC innovatively combines a perception module, which processes RGBD images for semantic segmentation and generates bird's eye view (BEV) mappings, with a controller module that utilizes these insights along with GNSS and angular speed measurements to accurately predict navigational waypoints. This integration allows DeepIPC to efficiently translate complex environmental data into actionable driving commands. Our comprehensive evaluation demonstrates DeepIPC's superior performance in terms of drivability and multi-task efficiency across diverse real-world scenarios, setting a new benchmark for end-to-end autonomous driving systems with a leaner model architecture. The experimental results underscore DeepIPC's potential to significantly enhance autonomous vehicular navigation, promising a step forward in the development of autonomous driving technologies. For further insights and replication, we will make our code and datasets available at //github.com/oskarnatan/DeepIPC.

In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the distance selection problem is to find the $k$-th smallest interpoint distance among all pairs of points of $P$. The previously best deterministic algorithm solves the problem in $O(n^{4/3} \log^2 n)$ time [Katz and Sharir, SIAM J. Comput. 1997 and SoCG 1993]. In this paper, we improve their algorithm to $O(n^{4/3} \log n)$ time. Using similar techniques, we also give improved algorithms on both the two-sided and the one-sided discrete Fr\'{e}chet distance with shortcuts problem for two point sets in the plane. For the two-sided problem (resp., one-sided problem), we improve the previous work [Avraham, Filtser, Kaplan, Katz, and Sharir, ACM Trans. Algorithms 2015 and SoCG 2014] by a factor of roughly $\log^2(m+n)$ (resp., $(m+n)^{\epsilon}$), where $m$ and $n$ are the sizes of the two input point sets, respectively. Other problems whose solutions can be improved by our techniques include the reverse shortest path problems for unit-disk graphs. Our techniques are quite general and we believe they will find many other applications in future.

Current studies on human locomotion focus mainly on solid ground walking conditions. In this paper, we present a biomechanic comparison of human walking locomotion on solid ground and sand. A novel dataset containing 3-dimensional motion and biomechanical data from 20 able-bodied adults for locomotion on solid ground and sand is collected. We present the data collection methods and report the sensor data along with the kinematic and kinetic profiles of joint biomechanics. A comprehensive analysis of human gait and joint stiffness profiles is presented. The kinematic and kinetic analysis reveals that human walking locomotion on sand shows different ground reaction forces and joint torque profiles, compared with those patterns from walking on solid ground. These gait differences reflect that humans adopt motion control strategies for yielding terrain conditions such as sand. The dataset also provides a source of locomotion data for researchers to study human activity recognition and assistive devices for walking on different terrains.

Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov Chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme can prevent being trapped in local optima through a series of intermediate posteriors. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.

In the past decade, we have witnessed the rise of deep learning to dominate the field of artificial intelligence. Advances in artificial neural networks alongside corresponding advances in hardware accelerators with large memory capacity, together with the availability of large datasets enabled researchers and practitioners alike to train and deploy sophisticated neural network models that achieve state-of-the-art performance on tasks across several fields spanning computer vision, natural language processing, and reinforcement learning. However, as these neural networks become bigger, more complex, and more widely used, fundamental problems with current deep learning models become more apparent. State-of-the-art deep learning models are known to suffer from issues that range from poor robustness, inability to adapt to novel task settings, to requiring rigid and inflexible configuration assumptions. Ideas from collective intelligence, in particular concepts from complex systems such as self-organization, emergent behavior, swarm optimization, and cellular systems tend to produce solutions that are robust, adaptable, and have less rigid assumptions about the environment configuration. It is therefore natural to see these ideas incorporated into newer deep learning methods. In this review, we will provide a historical context of neural network research's involvement with complex systems, and highlight several active areas in modern deep learning research that incorporate the principles of collective intelligence to advance its current capabilities. To facilitate a bi-directional flow of ideas, we also discuss work that utilize modern deep learning models to help advance complex systems research. We hope this review can serve as a bridge between complex systems and deep learning communities to facilitate the cross pollination of ideas and foster new collaborations across disciplines.

We address the task of automatically scoring the competency of candidates based on textual features, from the automatic speech recognition (ASR) transcriptions in the asynchronous video job interview (AVI). The key challenge is how to construct the dependency relation between questions and answers, and conduct the semantic level interaction for each question-answer (QA) pair. However, most of the recent studies in AVI focus on how to represent questions and answers better, but ignore the dependency information and interaction between them, which is critical for QA evaluation. In this work, we propose a Hierarchical Reasoning Graph Neural Network (HRGNN) for the automatic assessment of question-answer pairs. Specifically, we construct a sentence-level relational graph neural network to capture the dependency information of sentences in or between the question and the answer. Based on these graphs, we employ a semantic-level reasoning graph attention network to model the interaction states of the current QA session. Finally, we propose a gated recurrent unit encoder to represent the temporal question-answer pairs for the final prediction. Empirical results conducted on CHNAT (a real-world dataset) validate that our proposed model significantly outperforms text-matching based benchmark models. Ablation studies and experimental results with 10 random seeds also show the effectiveness and stability of our models.

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.

Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.